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 Trigonometry-basics/510165: -8i _____ 1+ 3i simplify. Answers should be in standard a + bi form1 solutions Answer 341733 by solver91311(16897)   on 2011-10-05 18:30:56 (Show Source): You can put this solution on YOUR website! Why did you make multiple submissions? John My calculator said it, I believe it, that settles it
 Trigonometry-basics/510166: -8i _____ 1+ 3i simplify. Answers should be in standard a + bi form1 solutions Answer 341732 by solver91311(16897)   on 2011-10-05 18:30:42 (Show Source): You can put this solution on YOUR website! Why did you make multiple submissions? John My calculator said it, I believe it, that settles it
 Polynomials-and-rational-expressions/510157: find the value of the discriminant and nature of the solutions. -6x^2+10x+10=01 solutions Answer 341730 by solver91311(16897)   on 2011-10-05 18:29:44 (Show Source): You can put this solution on YOUR website! For any quadratic polynomial equation of the form: Find the Discriminant, and evaluate the nature of the roots as follows: No calculation quick look: If the signs on and are opposite, then guaranteed. Two real and unequal roots. If is a perfect square, the quadratic factors over (the rationals). One real root with a multiplicity of two. That is to say that the trinomial is a perfect square and has two identical factors. Presuming rational coefficients, the root will be rational as well. A conjugate pair of complex roots of the form where is the imaginary number defined by John My calculator said it, I believe it, that settles it
 Geometric_formulas/510159: F= 9/5C+32 HOW i SOLVE the formula for Degrees Celcius C. please Show all steps1 solutions Answer 341728 by solver91311(16897)   on 2011-10-05 18:26:27 (Show Source): You can put this solution on YOUR website! Add to both sides. Multiply both sides by John My calculator said it, I believe it, that settles it
 Miscellaneous_Word_Problems/510130: Your club is selling candles to raise money. It costs $100 to rent a booth to sell candles. If the candles cost$1 each and are sold for $5 each, how many candle must be sold to equal your expenses?1 solutions Answer 341727 by solver91311(16897) on 2011-10-05 18:24:26 (Show Source): You can put this solution on YOUR website! The cost as a function of the number of candles bought is 1 dollar per candle bought plus 100 dollars for the rental of the booth. Let represent the number of candles bought, then . Let represent the number sold and this number is restricted to since you can't sell more than you buy. The revenue received is 5 dollars per candle sold, so the revenue function is Profit is Revenue minus Cost, so: Breakeven, that is when profit equals zero is when cost equals revenue: Now if what you really wanted to know (but didn't ask, or didn't communicate effectively anyway) is what is the number to buy such that if you sell them all, you break even? For that, you set , that is: Now just solve for . Note that if you only buy that many, the BEST you can do is break even. Since the general idea of any business venture, whether for profit or for charity, is to make money, you have to buy more than this. However, this comes with risk. The more you buy, the more you have to sell in order to turn a profit. What you really need now is the services of a market research firm that can tell you, within certain statistical limits, what your demand function is. That is, at any given price point within some sort of reasonable limits, how many candles you can expect to sell. John My calculator said it, I believe it, that settles it  Angles/510128: If the measure of an angle is 44°, then the angle is acute1 solutions Answer 341715 by solver91311(16897) on 2011-10-05 17:57:59 (Show Source): You can put this solution on YOUR website! What a fascinating little tidbit of not-very-arcane mathematical lore. Was there a question somewhere in our future? Did you actually read the instructions for posting that say you are supposed to make sure it is clear what it is you want and what you don't understand? John My calculator said it, I believe it, that settles it  Linear-equations/510122: 1. Find the slope of the line that passes through (-4,-8) and (-4,2). I was thinking its zero but "undefined" is also a choice. 2. Find the slope of the line that passes through (-4,2) and (2,2). Again, I think its either zero or "undefined" 1 solutions Answer 341712 by solver91311(16897) on 2011-10-05 17:56:00 (Show Source): You can put this solution on YOUR website! The slope is a fraction -- the difference of the y-coordinates divided by the difference of the x-coordinates. How do you describe a fraction with a denominator of zero? For your second problem, what is the value of a fraction where the numerator is zero? John My calculator said it, I believe it, that settles it  Linear-equations/510123: are (-2,5) and (6,-2)parallel,perpendicular, or neither to (-3,6) and (4,0)1 solutions Answer 341710 by solver91311(16897) on 2011-10-05 17:53:28 (Show Source): You can put this solution on YOUR website!Why did you ask the same question three times?  Linear-equations/510121: are (-2,5) and (6,-2)parallel,perpendicular, or neither to (-3,6) and (4,0)1 solutions Answer 341709 by solver91311(16897) on 2011-10-05 17:52:57 (Show Source): You can put this solution on YOUR website!Why did you ask the same question twice?  Linear-equations/510125: are (-2,5) and (6,-2)parallel,perpendicular, or neither to (-3,6) and (4,0)1 solutions Answer 341708 by solver91311(16897) on 2011-10-05 17:52:39 (Show Source): You can put this solution on YOUR website!Why did you ask the same question twice?  Triangles/510092: if the area of a triangle is 5in than what is the base and hight of the triangle? how did u get the answer?1 solutions Answer 341707 by solver91311(16897) on 2011-10-05 17:51:06 (Show Source): You can put this solution on YOUR website! No way to tell. All you know is that the product of the base and the height is 10, but there are an infinite number of pairs of such numbers whose product is 10. John My calculator said it, I believe it, that settles it  Rectangles/510106: A CLASS OF 42 STUDENTS AND 2 TEACHERS PLAN A TRIP TO AN OBSERVATORY. THE CLASS RAISED$485 FOR TGE TRIP. ADMISSION IS $5 PER PERSON AND THE BUS RENTAL IS$230. WITH THE REMAINING MONEY, THE CLASS CAN INVITE GUEST TO FILL THE REMAINING SEATS ON THE BUS. WRITE AND SOLVE AN EQUATION TO FIND THE NUMBER OF GUEST THE CLASS CAN INVITE. LET THE G REPRESSNT GUEST 1 solutions Answer 341701 by solver91311(16897)   on 2011-10-05 17:22:01 (Show Source): You can put this solution on YOUR website!WHY DO YOU FIND IT NECESSARY TO SHOUT?
 Length-and-distance/510101: How do you find the distance between x+3y=6 and x+3y=-14 if they are both parallel lines?1 solutions Answer 341700 by solver91311(16897)   on 2011-10-05 17:21:18 (Show Source): You can put this solution on YOUR website! Pick a point on either line. Write an equation of a line that passes through the point you selected and is perpendicular to the line containing that point. Remember, the slopes of perpendicular lines are negative reciprocals of each other. Use the point-slope form: where are the coordinates of the given point and is the given/calculated slope. Once you have the equation of the perpendicular to the line you chose at the start, solve the system of equations formed by the OTHER given line and the perpendicular. The solution set of the above described system is the point of intersection between the perpendicular and the line NOT chosen in the first step. Find the distance from the point you selected in the first step and the point of intersection that you just calculated. Use the distance formula: where and are the coordinates of the two points of intersection. John My calculator said it, I believe it, that settles it
 Graphs/510097: how do you write an equation of the line that passes through each pair of points? Ex. (0,-4),(5,-4)1 solutions Answer 341696 by solver91311(16897)   on 2011-10-05 17:10:00 (Show Source): You can put this solution on YOUR website! Use the two-point form of an equation of a line: where and are the coordinates of the given points. John My calculator said it, I believe it, that settles it
 Linear-equations/509968: Please show all work, Find the slope and y-intercept of the line x=5y=81 solutions Answer 341677 by solver91311(16897)   on 2011-10-05 14:01:47 (Show Source): You can put this solution on YOUR website! Sorry, is not a line nor is it a representation of a line. One of those equals signs needs to be either a + or a -. Given the configuration of the standard keyboard and no indication of whether you meant the equation to be in standard form or not, there are 4 possibilities and I'm not going to work all 4. Given that, you can do this yourself. Start with the correct equation and then solve it for , which is to say use whatever algebraic manipulations are required to get by itself on the left side of the equals sign and everything else on the right side. You will end up with something that has this pattern: The slope is then , the coefficient on , and the -intercept is the point , where is the constant term in the right hand side. John My calculator said it, I believe it, that settles it
 Graphs/509965: How do I graph the following equations: Y= 25x +100 Y=50x1 solutions Answer 341675 by solver91311(16897)   on 2011-10-05 13:53:16 (Show Source): You can put this solution on YOUR website! The following procedure works for either of them: Step 1. Pick a value for x. It can be anything you like, but 0, 1, or some other small integer usually works well and makes the arithmetic easier. Step 2. Substitute that value in place of x in your equation. Do the arithmetic and determine the value of y that results. Step 3. Take the value of x that you selected for step 1 and the value of y that you calculated in step 2 and form an ordered pair (x,y). Step 4. Plot the ordered pair from Step 3 on your graph. Remember that the x value is the distance right or left along the horizontal axis and the y value is the distance up or down along the vertical axis. Step 5. Repeat steps 1 through 4 with a different value for x. Step 6. Draw a line across your graph that passes through the two points that you plotted. John My calculator said it, I believe it, that settles it
 Square-cubic-other-roots/509958: Dear Sir/Madam: I hope I have selected the appropriate topic for my question which is: I know the square footage of a room is 450 square feet. How do I find the length and the width? Thank you. Pamela Jones email: pdj1998@aol.com1 solutions Answer 341674 by solver91311(16897)   on 2011-10-05 13:46:51 (Show Source): You can put this solution on YOUR website! You can't find the length and width only knowing the area. It could be a 20 foot by 22.5 foot nearly square room, or it could be an inch wide and 5400 feet long -- or anywhere in between. Now if you had some sense of the proportions, such as "the length is twice the width" or "the width is two and a half feet less than the length" or some other words to that general effect, THEN we can do something. John My calculator said it, I believe it, that settles it
 Functions/509959: What is the domain of 14(x+2)? 1 solutions Answer 341672 by solver91311(16897)   on 2011-10-05 13:38:45 (Show Source): You can put this solution on YOUR website! All real numbers except for any numbers that would make the expression undefined. John My calculator said it, I believe it, that settles it
 Equations/509960: solve for n: t=2n+2z1 solutions Answer 341671 by solver91311(16897)   on 2011-10-05 13:37:43 (Show Source): You can put this solution on YOUR website! Divide both sides by 2, then add to both sides. John My calculator said it, I believe it, that settles it
 Angles/509951: The leght of a rectangular road sing is 2 feet less than three times its width. Find the dimensions if the perimeter is 28 feet.1 solutions Answer 341670 by solver91311(16897)   on 2011-10-05 13:36:16 (Show Source): You can put this solution on YOUR website! Did you use your spell randomizer on this one? And what is a 'road sing'? Not that it matters. Assuming you meant that the length is 2 feet less than three times the width, the dimensions of any rectangular fernblatz with the given proportions and given that the perimeter is 28 feet are found by using the formula for the perimeter: Here's what we know: and So put what we know into the formula: Solve for and then calculate John My calculator said it, I believe it, that settles it
 logarithm/509950: Write the following epression as a single logarithm: log5-logx-logy1 solutions Answer 341667 by solver91311(16897)   on 2011-10-05 13:24:06 (Show Source): You can put this solution on YOUR website! The sum of the logs is the log of the product, the difference of the logs is the log of the quotient. Rewrite your expression: Apply the sum rule: Apply the difference rule: John My calculator said it, I believe it, that settles it
 Word_Problems_With_Coins/509942: A bag of coins contains 30 coins, some dimes and some quarters. The total amount of money in the bag is $3.45. How many dimes and quarters are in the bag?1 solutions Answer 341665 by solver91311(16897) on 2011-10-05 13:19:55 (Show Source): You can put this solution on YOUR website! Let represent the number of quarters. Then, since there are 30 coins altogether and the only consist of dimes and quarters, the number of dimes must be . Each of the quarters has a value of 25 cents, so the total value of the quarters is cents. Likewise, the total value of the dimes is cents. The total value of all the coins is$3.45 which is to say 345 cents. Putting it all together: Solve for to find the number of quarters, then calculate to find the number of dimes. John My calculator said it, I believe it, that settles it
 Equations/509941: How do I work this equation? 7.5/x=.1216 1 solutions Answer 341663 by solver91311(16897)   on 2011-10-05 13:12:55 (Show Source): You can put this solution on YOUR website! Multiply both sides by x, then divide both sides by 0.1216. John My calculator said it, I believe it, that settles it
 Permutations/509918: Let x denote the exam scores of 10 students in Stat 230 and y the exam scores of 10 students in Stat 303. A reasonable value for r is (a) 0.7 (b) -0.7 (c) 0 (d) r is not applicable 'r' is the correlation coefficient right? But since the two are independent of each other I think the answer is c) 0? Is that the right way of thinking about it?1 solutions Answer 341662 by solver91311(16897)   on 2011-10-05 13:11:58 (Show Source): You can put this solution on YOUR website! By saying , you are saying there is no correlation whatsoever between 10 students' scores in an intermediate Stat class as compared to 10 students' scores in an advanced Stat class. Are the two truly independent of each other? Wouldn't you say that the the smart ones that bubble to the top in elementary and intermediate statistics would very likely continue to be more successful than their peers in the more advanced classes? Or looking at it the other way, what is the likelyhood that someone who is doing very well in advanced statistics is a person who struggled through the less difficult courses? That sort of empirical "gut feel" correlation has been my experience in every high school and college mathematics program with which I have been associated. If I were answering the question, I would say a) 0.7. John My calculator said it, I believe it, that settles it
 Probability-and-statistics/509903: here is the problem- A bowl contains 9 red marbles, 5 white marbles, and 3 blue marbles. If a person selects one marble from the bowl at random and draws a red marble, they lose $1.00. If a white marble is selected, they win$2.00, and if a blue one is selected, they win $3.00. WHat is the expected profit or loss for a person playing this game? I have done this a few different ways and am still not sure of what the question is really asking me.1 solutions Answer 341649 by solver91311(16897) on 2011-10-05 12:28:47 (Show Source): You can put this solution on YOUR website! The probability of drawing a red is , hence the payout for drawing a red is The probability of drawing a white is , hence the payout for drawing a white is The probability of drawing a blue is , hence the payout for drawing a blue is The overall expected payout is the sum of the three expected payouts caluclated above: . So what does that mean? If the owner of the game charges you$0.58 or less each time you play, then go for it (as long as the game owner can afford to run his loser, that is). On the other hand, if it costs $0.59 or more to play, walk away -- it is a loser for the player. John My calculator said it, I believe it, that settles it  Proportions/509904: My friend and I are mixing blue and white paint in order to get a lighter shade of blue.I use 2 cups of blue paint and 1 cup of white paint. my friend uses 3 cups of blue paint and 2 cups of white paint. Which mixture is darker?1 solutions Answer 341647 by solver91311(16897) on 2011-10-05 12:12:38 (Show Source): You can put this solution on YOUR website! Your way is 2 out of 3 (2 + 1) parts blue, or blue. Your friend's way is 3 out of 5 (3 + 2) parts blue, or . So which is bigger, or ? John My calculator said it, I believe it, that settles it  Triangles/509847: Thank you in advance. Need help, textbook show lousy examples to explain process needed to solve problem. This problem is confusing to me, The triangle appears to be scalene, there are no cong.sides of this triangle picture of the graph in the book. The question is Triangle ABC has vertices A(0,8), B (6,0), C(15,0) (B and C lie on the same line in the diagram, A is angled up toward the left then angles down to meet C) USE THE DISTANCE FORMULA to find; AB= AC= BC= what is the perimeter of triangle ABC=_____ what is the area of triangle ABC=______square units. 1 solutions Answer 341645 by solver91311(16897) on 2011-10-05 12:06:14 (Show Source): You can put this solution on YOUR website! The distance formula: where and are the coordinates of the given points. You have three points, so you have three pairs of points. Use the distance formula 3 times to calculate the measure of the three sides. Add the three measures to calculate the perimeter. The area is a little trickier. If you use segment BC as the base of the triangle, then the segment OA (Point O being the origin (0,0)) is the altitude of the triangle. Use the distance formula to calculate the measure of OA (or just do it by inspection of the graph) and then submit the base and altitude measures to the formula for the area of a triangle, namely the base times the altitude divided by 2. This triangle has a very interesting property. The number of linear units in the perimeter is equal to the number of square units in the area. John My calculator said it, I believe it, that settles it  Miscellaneous_Word_Problems/509606: Write an equation and solve for the word problem: Rico spent$18.50 to rent a lawn mower. The fee for the first hour was $8. Each additional hour cost$3.50. For how many hours did he rent the mower? I figured out the answer is 4 hours, but what is the equation that goes with this word problem?1 solutions Answer 341508 by solver91311(16897)   on 2011-10-04 20:59:10 (Show Source): You can put this solution on YOUR website! Solve for when John My calculator said it, I believe it, that settles it
 Finance/509587: how do you get 9.43 from the square root of 891 solutions Answer 341506 by solver91311(16897)   on 2011-10-04 20:53:43 (Show Source): You can put this solution on YOUR website! You don't. Saying is incorrect. In fact, saying , which is the answer the built-in Windows calculator gives, is also incorrect. Both are approximations, although one is much closer than the other. Since is an irrational number it is impossible to write it exactly as a decimal fraction. On the other hand, 9.43 is probably close enough for most purposes. Just looking at and not having a calculator, one way to go about it is to recognize that and , and since , . Then 89 is a little less than half-way from 81 to 100, so if you try 9.5 times 9.5 to get 90.25 (too big) and 9.4 times 9.4 to get 88.36 (too small), you know you have to be somewhere in between. Keep refining to as many decimal points as you like. John My calculator said it, I believe it, that settles it
 Travel_Word_Problems/509517: Amanda drove 50 miles. She decreased her speed by 20 mph and drove another 5 miles. If the entire trip took one hour and thirty minutes, at what rate(s) did Amanda drive?1 solutions Answer 341497 by solver91311(16897)   on 2011-10-04 20:28:43 (Show Source): You can put this solution on YOUR website! Use time equals distance divided by rate. Let represent the initial rate. Then the reduced rate is . Let represent the time it took to travel the first 50 miles. Then is the time it took to travel the last 5 miles. We know that and Substituting from the first equation: A little Algebra music, Sammy: Multiply by 2 and the quadratic factors rather tidily. One of the roots doesn't work because it is less than 20, which means that the rate would be negative (driving in reverse to go backwards in time?) for the 5 mile second leg of the trip. Solve for and then calculate John My calculator said it, I believe it, that settles it
 Equations/509508: Can you please solve this equation for me a: 5t/12=4-3t B: Prove your solution is correct? thank you :) 1 solutions Answer 341477 by solver91311(16897)   on 2011-10-04 19:32:54 (Show Source): You can put this solution on YOUR website! Multiply both sides by 12. Add to both sides. Multiply both sides by Leave the answer in fraction form otherwise you will be mucking about with a very ugly repeating decimal. Ew-w-w-w. Prove the answer: Take your solution and substitute it back into the original equation. Do all indicated arithmetic. You should get the same number on both sides of the equal sign. John My calculator said it, I believe it, that settles it